For starting completely empty, I could include the Ascot to Guildford shuttle, which connects out of the Waterloo service at Ascot. Originally a through service which divided there, both parts getting away within a couple of minutes, it is now a connection which allows 10 minutes. However the Waterloo service, if delayed along the way, is quite often 10 minutes late arriving. I've been travelling to Camberley and have seen it all, including slamming the doors and going when just half the connecting passengers have made it across between platforms, or even setting off just as the first one runs up. Nobody ever starts their journey at Ascot, so it's empty.
I did once read of the Stourbridge shuttle, which likewise only really services connecting passengers, being sent off from the Junction on time, with the inbound main service just pulling in, but was following instructions. Having arrived at Stourbridge Town on time, albeit empty, it then went straight back as an extra service, to pick up the passengers ...